1095-B and filing Separately

A Form 1095-B is not entered on a tax return.

If you and he are filing as Married Filing Separately then he will need your Social Security number to file his tax return and you will need his Social Security number to file your tax return.

If you were still married on Dec 31, 2022 and you don't file a joint return you will need to enter each other's ssn on your MFS Married filing Separate returns.  So yes he needs your ssn and you need his.

You don't enter a 1095B or C into a tax return.  Only enter a 1095A form.   Ignore the 1095B.